{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T23:09:12Z","timestamp":1778368152925,"version":"3.51.4"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032190956","type":"print"},{"value":"9783032190963","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":90,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Evaluating machine learning (ML) model bias is key to building trustworthy and robust ML systems. Counterfactual Fairness (CF) audits allow the measurement of bias of ML models with a causal framework, yet their conclusions rely on a single causal graph that is rarely known with certainty in real-world scenarios. We propose CF with Graph Uncertainty (CF-GU), a bias evaluation procedure that incorporates the uncertainty of specifying a causal graph into CF. CF-GU (i) bootstraps a Causal Discovery algorithm under domain knowledge constraints to produce a bag of plausible Directed Acyclic Graphs (DAGs), (ii) quantifies graph uncertainty with the normalized Shannon entropy, and (iii) provides confidence bounds on CF metrics. Experiments on synthetic data show how contrasting domain knowledge assumptions support or refute audits of CF, while experiments on real-world data (COMPAS and Adult datasets) pinpoint well-known biases with high confidence, even when supplied with minimal domain knowledge constraints.<\/jats:p>","DOI":"10.1007\/978-3-032-19096-3_19","type":"book-chapter","created":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T22:18:47Z","timestamp":1778365127000},"page":"294-310","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Counterfactual Fairness with\u00a0Graph Uncertainty"],"prefix":"10.1007","author":[{"given":"Davi","family":"Val\u00e9rio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chrysoula","family":"Zerva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariana","family":"Pinto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Santos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9","family":"Carreiro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"19_CR1","doi-asserted-by":"crossref","unstructured":"Andrews, B., Ramsey, J., Sanchez\u00a0Romero, R., Camchong, J., Kummerfeld, E.: Fast scalable and accurate discovery of dags using the best order score search and grow shrink trees. In: Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., Levine, S. (eds.) Advances in Neural Information Processing Systems. vol.\u00a036, pp. 63945\u201363956. Curran Associates, Inc. (2023)","DOI":"10.52202\/075280-2794"},{"key":"19_CR2","unstructured":"Angwin, J., Larson, J., Mattu, S., Kirchner, L.: Machine bias. ProPublica (2016). https:\/\/www.propublica.org\/article\/machine-bias-risk-assessments-in-criminal-sentencing"},{"key":"19_CR3","unstructured":"Barocas, S., Hardt, M., Narayanan, A.: Fairness and machine learning: limitations and opportunities. MIT press (2023)"},{"key":"19_CR4","unstructured":"Becker, B., Kohavi, R.: Adult. UCI Machine Learning Repository (1996)"},{"key":"19_CR5","unstructured":"Binkyt\u0117, R., Makhlouf, K., Pinz\u00f3n, C., Zhioua, S., Palamidessi, C.: Causal Discovery for Fairness. In: Proceedings of the Workshop on Algorithmic Fairness through the Lens of Causality and Privacy, pp. 7\u201322. 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